A lamina occupies the part of the disk x2+y2=1 in the first quadrant. Find its center of mass if the density at any point is proportional to its distance from the x-axis

Q: Suppose that a cylindrical container of radius r and height L is filled with a liquid with volume V…

A: Consider the given:  Express volume in terms of “h”, “r” and “w”.…

Q: Find the centroid of a thin, flat plate covering the region enclosed by the parabola y2 = x and the…

A: Given information:

Q: Kepler's Third Law states that the ratio T/a³/2 is equal to a con- stant C for all planetary orbits…

A: Given :        Ta32 = C , where T is the period and a is the semimajor axis.

Q: Find the centroid of the triangular region cut from the first quadrant by the line x + y = 3.

A: We will find the x and y-intercept of the triangle.  To find x-intercept we plug y=0 and find x…

Q: Parametrize a circular spiral centered at the z-axis, starting at (0,2,0) and ending at (0,2,12)…

A: As per the question we have to find the 3d parametric equation of a spiral centred at the z-axis…

Q: Determine the centroid in the y

A:

Q: Find the centroid of the region bounded by the parabola y=x? and the line y=4.

A:

Q: Find the area of the surface when y = vx, from (4, 2) to (9, 3) is rotated about the x-axis.

A: Surface area formula for rotating about x-axis is S=∫2πydS where dS=1+dydx2dx

Q: Locate the Centroid of the area bounded by the x-axis, the line x=4, and the parabola y2 = x.

A: We have to find the centroid of the area bounded by curve.

Q: A thin plate (R) occupies the smaller region cut from the ellipse x² +4y² =12 by the parabola x =…

A: Given that a thin plate  (R) occupies the smaller region cut from the ellipse x2+4y2=12 by…